Visualization of high-dimensional data is an important step in exploratory data analysis and knowledge discovery. However, it is challenging, because the interpretation is highly subjective. If we see dimensionality reduction (DR) techniques as the main tool for data visualization, they are like multiple cameras that look into the data from different perspectives or angles. We can hardly prescribe one single perspective for all datasets and problems. One snapshot of data cannot reveal all the relevant aspects of the data in higher dimensions. The reason is that each of these methods has its own specific strategy, normally based on well-established mathematical theories to obtain a low-dimensional projection of the data, which sometimes is totally different from the others. Therefore, relying only on one single projection can be risky, because it can close our eyes to important parts of the full knowledge space. We propose the first framework for multi-insight data visualization of multi-omics data. This approach, contrary to single-insight approaches, is able to uncover the majority of data features through multiple insights. The main idea behind the methodology is to combine several DR methods via tensor factorization and group the solutions into an optimal number of clusters (or insights). The experimental evaluation with low-dimensional synthetic data, simulated multi-omics data related to ovarian cancer, as well as real multi-omics data related to breast cancer show the competitive advantage over state-of-the-art methods. https://folk.uio.no/hadift/MIV/ [user/pass via hadift@medisin. uio.no] Supplementary data are available at Bioinformatics online.